I am wondering what is the antidote to loneliness, or the approach towards it, within Buddhism.
In Buddhism loneliness is viewed and treated exactly as any other undesirable mindstate.
What are the things that cause loneliness and exacerbate it?
Any mental activity that involves "feeding" (sustaining) the description or image of the world as such that considers socializing to be a core valuable activity, would naturally cause the feeling of loneliness. This includes watching TV series and using social media. Also, as ChrisW said - comparing one's situation to others who are social, attachment to past pleasant social experiences. All this can be summarized as unwise application of attention which serves as feeding/sustenance of craving.
What are the non-social antidotes to loneliness?
The same old trick, wise application of attention. Moving one's perception into position where the problem of loneliness does not exist. The possibilities are infinite, from getting oneself involved with abstract sciences, to computer programming, creative performance and art, music -- to convincing oneself that loneliness is not only acceptable, but in fact natural for persons of high realization and beneficial for their well-being -- to direct Jhana experience of reviewing one's mental continuum and praising it for the absence of typical ups and downs that would have inevitably accompanied socializing.
(2) Does active and directed attention, whether in meditation or attending to tasks, alleviate feelings of loneliness in the long term?
Yes, exactly. See above.
(3) what is the Buddhist view on social media use? Is it inherently fragmenting awareness as I suspect? Does it have no benefits?
Mahayana view would be, that as long as your motivation is to help others, the use of social networks is appropriate, even if it causes you personal pain. In other words, Mahayana is totally fine with paying the price of suffering for the higher goal of helping others reduce theirs. This thought in itself reduces personal suffering.
Of course it fragments awareness. But this is the spirit of times, and we want to be in tune with it if we are to be relevant.